A car is parked by an owner amongst 25 cars in a row, not at either end. On his return he finds that exactly 15 places are still occupied. The probability that both the neighboring places are empty  is

A car is parked by an owner amongst 25 cars in a row, not at either end. On his return he finds that exactly 15

 places are still occupied. The probability that both the neighboring places are empty  is

  1. A

    91276

  2. B

    15184

  3. C

    1592

  4. D

    none of these

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    Solution:

    t is given that 15 places are occupied. This includes the owner's car also, and, hence 14 other cars are parked.

     There are 24 places (excluding places at the two ends) out of which 14 places can be chosen in  22C14   ways.

     Excluding 15 (c) 92 (d) none of these the neighboring places there are 22 places in which 14 cars can be

     parked in 22C14  ways 

    Hence, required probability = 22C14 24C14=1592 

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